A system of physical chemistry - Index of

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A system of physical chemistry - Index of

EQ UIPARTITION OF KINE TIC ENERG Y 2 5

an unknown number in respect of rotation and vibration. We pass on,

therefore, to the solid state. In the case of a soUd, i.e. a crystalline

substance, and probably

also in the case of a super- cooled liquid like

glass, it is necessary to regard translational energy (and also rotational

energy) as absent, the energy possessed by the molecules of a solid

being vibrational. As already stated, vibration of each atom can take

place along all three axes, so that even the simplest type of solid

possesses three degrees of freedom. We shall return to this later.

For the present we have to take up the application of the principle

of equipartition of (kinetic) energy amongst degrees of freedom. According

to this principle, when a system is in statistical equilibrium, such

equilibrium being determined by a number of variables, i.e. degrees of

freedom, to each such variable one must attribute the same quantity of

{kinetic) energy. It is to be remembered that there is no restriction as

regards the physical state of the system— the principles applies equally

well to gaseous, liquid, or solid systems and to systems embracing two

or more such states simultaneously. It is supposed to hold equally

well also for degrees of freedom in respect of translation, vibration, or

rotation. To see how much this energy amounts to per degree of

freedom, let us consider the kinetic energy of translation of a perfect

gas at a given temperature. First of all we have the relation—

PV = RT.

Further, we have seen in the theoretical deduction of Boyle's Law

that—

P = \pu^

where is the density of the gas and u the root-mean-square velocity.

.

,

we are considermg i gram-molecule of the gas, p =

molecular weight (M)

where V is the molecular volume, and hence we can write—

• PV = JM?

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